Method for predicting band structure and optical properties of graphene nanoribbons

Abstract

The application discloses a method for predicting the band structure and optical properties of graphene nanoribbons, comprising the following steps: establishing a graphene model, constructing an atomic structure model of the graphene nanoribbons by adding a vacuum layer, cutting and edge-hanging hydrogen atoms; based on the atomic structure model of the graphene nanoribbons, a structure with the lowest system energy is optimized by using the first principle to obtain the optimized graphene nanoribbons; the charge density and the electron wave function of the optimized graphene nanoribbons are calculated by using the density functional theory; the band structure and the electronic state density of the graphene nanoribbons are calculated according to the electron wave function; and the optical properties of the graphene nanoribbons are calculated according to the charge density. Compared with actual measurement, the method can avoid the interference of external factors in the test process, can avoid the problems that the edge structure and the width are difficult to control in the manufacturing process of the graphene nanoribbons, and has higher efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of graphene material calculation, and particularly relates to a prediction method for band structure and optical properties of graphene nanoribbons. BACKGROUND

[0002] Since Novoselov et al. successfully prepared single-layer graphene in 2004, graphene has been active in various applications in the material field due to its unique properties, such as electrical conductivity and thermal conductivity. Meanwhile, the preparation of nanomaterials around graphene has also been very popular, and graphene nanoribbons are a typical graphene nanomaterial.

[0003] Graphene nanoribbons are quasi-one-dimensional carbon nanomaterials, and the boundary effect has a great impact on them, which is the main factor determining the electronic structure; and the electronic structure determines other physical properties, including optical properties and electromagnetic properties. The boundary effect endows graphene nanoribbons with more unique properties than traditional graphene materials, and also makes them have a very broad application prospect in various fields, so it is very important to analyze the electronic structure of graphene nanoribbons and their related physical properties.

[0004] Graphene nanoribbons can be divided into armchair graphene nanoribbons (AGNRs) and zigzag graphene nanoribbons (ZGNRs) according to their edge structures. At present, the methods for synthesizing graphene nanoribbons include cutting carbon nanotubes and template synthesis, but it is still very difficult to control the width and edge structure, and the synthesis technology is not mature enough. Therefore, using the method of computational materials science to predict the properties of graphene nanoribbons with a certain width and edge structure can greatly reduce the workload of traditional preparation and testing experiments, and provide theoretical guidance for the application of graphene nanoribbons in optics. SUMMARY

[0005] In view of the needs in the prior art, the application provides a prediction method for band structure and optical properties of graphene nanoribbons.

[0006] The technical scheme adopted by the application is as follows:

[0007] A prediction method for band structure and optical properties of graphene nanoribbons comprises the following steps:

[0008] S1, a graphene model is established, and an atomic structure model of graphene nanoribbons is constructed by adding a vacuum layer, cutting, and edge-hanging hydrogen atoms;

[0009] S2, based on the atomic structure model of the graphene nanoribbon, a structure with the lowest system energy is optimized by using the first principle to obtain the optimized graphene nanoribbon;

[0010] S3, the charge density and the electron wave function of the optimized graphene nanoribbon are calculated by using the density functional theory;

[0011] S4, the band structure and the electron state density of the graphene nanoribbon are calculated according to the electron wave function; and the optical property of the graphene nanoribbon is calculated according to the charge density.

[0012] Further, the optical property includes the dielectric function, the absorption rate, the reflectivity, the transmissivity and the energy loss spectrum.

[0013] Further, the step S1 specifically includes

[0014] The atomic structure model of the graphene nanoribbon is constructed by using the software Materials Studio: the graphite crystal is introduced, the symmetry between the graphite layers is eliminated and the extra graphite layers are deleted, one layer is reserved to form the single-layer graphene; a vacuum layer with a thickness of 20 angstrom is added in the direction perpendicular to the single-layer graphene to constitute the completely independent single-layer graphene, the unit cell is expanded to obtain the graphene model with the six-membered ring network structure;

[0015] The graphene is cut, in the cutting process, when the cutting plane only passes through the nodes of the carbon six-membered ring, the graphene nanoribbon with the zigzag edge structure is obtained; in the cutting process, when the cutting plane only passes through the carbon-carbon single bond of the carbon six-membered ring, the graphene nanoribbon with the armchair edge structure is obtained; according to the position of the cutting plane, the width of the graphene nanoribbon obtained by cutting is determined;

[0016] After the cutting of the graphene nanoribbon is completed, the chemical bond of the graphene nanoribbon is saturated by suspending the hydrogen atom on the edge unsaturated carbon atom.

[0017] Further, the step S2 includes: exporting the atomic coordinate file POSCAR of the graphene nanoribbon model established by the Materials Studio through the software VESTA to become the operation initial file of the software VASP, importing the operation initial file into the software VASP, and performing the structure optimization by using the software VASP to obtain the optimized graphene nanoribbon structure which is output in the form of the CONTCAR file.

[0018] Further, the operation initial file further includes the parameter setting file INCAR, the atomic pseudo-potential file POTCAR and the K-point selection file KPOINTS; when the structure optimization is performed by using the software VASP, the PAW pseudo-potential is selected, the GGA calculation processing exchange correlation energy function is adopted, and the functional selection is GGA-PBE. ​

[0019] Further, the step S3 comprises: obtaining a converged charge density and an electronic wave function through static self-consistent calculation by iteration; the self-consistent calculation adopts a density functional theory to obtain the electronic wave function and the charge density distribution of the ground state by solving a Schrodinger equation.

[0020] Further, the CONTCAR file obtained in the step S2 is named as POSCAR as new structure information, calculation parameters are given in the INCAR file, and static self-consistent calculation is performed through the software VASP.

[0021] An attempt charge density and an attempt electronic wave function are generated, an expression of an exchange correlation potential is written based on the attempt charge density and the attempt electronic wave function, and a Hamiltonian is constructed according to the charge density;

[0022] The electronic wave function is iteratively optimized to be closer to the exact electronic wave function of the Hamiltonian through subspace diagonalization or iterative diagonalization.

[0023] A new charge density is calculated according to the optimized electronic wave function, and then compared with the attempt charge density; if the result converges, the electronic wave function and the charge density are output; if the result does not reach the convergence accuracy, a round of calculation is performed again until the result reaches the convergence accuracy or the number of iterations reaches a set maximum value.

[0024] Further, when performing the static self-consistent calculation through the software VASP, a PAW pseudo-potential is selected, a GGA calculation is used to process an exchange correlation energy function, and a functional is selected as GGA-PBE.

[0025] The charge density data of the calculated ground state graphene nanoribbon is stored in CHG and CHGCAR files, and the electronic wave function data is stored in a WAVECAR file.

[0026] Further, in the step S4, the WAVECAR file is input into the software VASP, and calculation is performed after the INCAR file is set; in this process, the meaning of KPOINTS is a path for calculating energy bands, and the path is required to span the entire Brillouin zone; the calculated electronic state density and band structure data are output in a vasprun.xml file, and the data are extracted and plotted to obtain the electronic state density and band structure diagram.

[0027] Further, in the step S4, a dielectric function is obtained based on the charge density, and then a real part and an imaginary part matrix of the dielectric function are obtained; the absorption rate, the reflectivity, the transmissivity, and the energy loss spectrum of the graphene nanoribbon are calculated through the real part and the imaginary part matrix of the dielectric function.

[0028] Compared with the prior art, the present application has the following beneficial effects:

[0029] The application provides a method for calculating energy band structure and optical property of graphene nanoribbons by using first principle and density functional theory, and starting from basic physical laws.

[0030] In addition, the application is more accurate in analyzing optical property of graphene nanoribbons, can explore more profound application of graphene nanoribbons in the optical aspect, and provides technical support for application of graphene nanoribbons in the photoelectric field. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows, and the features and advantages of the application will be more clearly understood by referring to the drawings. The drawings are schematic and should not be understood as any limitation on the application. Those skilled in the art can obtain other drawings according to the drawings without any creative effort. Among them:

[0032] Figure 1 The flow chart of the graphene nanoribbon energy band structure and optical property prediction method described in the embodiments of the application;

[0033] Figure 2 The principle diagram of the iterative calculation of the ground state electron density by using VASP in the embodiments of the application;

[0034] Figure 3 The interface schematic diagram of the atomic model construction software Materials Studio used in the embodiments of the application;

[0035] Figure 4 The graphene nanoribbon model constructed in the embodiments of the application, wherein (a) is a graphene nanoribbon (AGNR) with armchair edge structure, and (b) is a graphene nanoribbon (ZGNR) with zigzag edge structure;

[0036] Figure 5 The interface schematic diagram of the VESTA interface of the input structure file of VASP calculation constructed in the embodiments of the application;

[0037] Figure 6 The input file (left side) and the output file (right side) of the software VASP in the structure optimization step of the embodiments of the application;

[0038] Figure 7The electronic state density diagram of the graphene nanoribbon constructed in the embodiment of the present application, wherein (a) is the electronic state density diagram of the armchair edge structure graphene nanoribbon (AGNR), and (b) is the electronic state density diagram of the zigzag edge structure graphene nanoribbon (ZGNR);

[0039] Figure 8 The band structure diagram of the graphene nanoribbon constructed in the embodiment of the present application, wherein (a) is the band structure of the armchair edge structure graphene nanoribbon (AGNR), and (b) is the band structure of the zigzag edge structure graphene nanoribbon (ZGNR);

[0040] Figure 9 The dielectric function image of the graphene nanoribbon constructed in the embodiment of the present application, wherein (a) is the dielectric function image of the armchair edge structure graphene nanoribbon (AGNR), and (b) is the dielectric function image of the zigzag edge structure graphene nanoribbon (ZGNR);

[0041] Figure 10 The absorption rate image of the graphene nanoribbon constructed in the embodiment of the present application, wherein (a) is the absorption rate image of the armchair edge structure graphene nanoribbon (AGNR), and (b) is the absorption rate image of the zigzag edge structure graphene nanoribbon (ZGNR);

[0042] Figure 11 The reflectivity image of the graphene nanoribbon constructed in the embodiment of the present application, wherein (a) is the reflectivity image of the armchair edge structure graphene nanoribbon (AGNR), and (b) is the reflectivity image of the zigzag edge structure graphene nanoribbon (ZGNR);

[0043] Figure 12 The transmittance image of the graphene nanoribbon constructed in the embodiment of the present application, wherein (a) is the transmittance image of the armchair edge structure graphene nanoribbon (AGNR), and (b) is the transmittance image of the zigzag edge structure graphene nanoribbon (ZGNR);

[0044] Figure 13 The energy loss spectrum of the graphene nanoribbon constructed in the embodiment of the present application, wherein (a) is the energy loss spectrum of the armchair edge structure graphene nanoribbon (AGNR), and (b) is the energy loss spectrum of the zigzag edge structure graphene nanoribbon (ZGNR); DETAILED DESCRIPTION

[0045] In order to enable the above-mentioned objects, features and advantages of the present application to be more clearly understood, the present application will be described in further detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0046] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one skilled in the art that the present application can be practiced without the specific details set forth in this description.

[0047] Referring to the drawings Figure 1 The method for predicting the energy band structure and optical properties of graphene nanoribbons of the present application comprises the following steps:

[0048] Step 1, constructing an atomic structure model of graphene nanoribbons with different edge structures;

[0049] Step 2, optimizing the structure to the lowest energy of the system by using the first principle;

[0050] Step 3, calculating the charge density and electron wave function of the graphene nanoribbons after structure optimization according to the density functional theory;

[0051] Step 4, obtaining the electron density of states and energy band structure by using the electron wave function, and calculating the optical properties of the graphene nanoribbons including the dielectric function, absorption rate, reflectivity, transmissivity, energy loss spectrum, etc. by using the charge density.

[0052] Specifically, referring to the drawings Figure 1 and Figure 2 In one embodiment of the present application, the method for predicting the energy band structure and optical properties of graphene nanoribbons comprises the following steps:

[0053] Step 1, using the software Materials Studio (hereinafter referred to as MS) to establish a model of graphene nanoribbons (Fig. 1 is the use interface of MS). Figure 3 Fig. 1 is the use interface of MS.

[0054] The process of establishing graphene nanoribbons is as follows: first, establish a graphene model, introduce a graphite crystal through the MS material library, wherein the MS material library stores a classical crystal structure model, and the cell parameters and other data thereof are obtained based on the actual crystal. After introducing the graphite crystal, eliminate the symmetry between the graphite layers and delete the excess graphite layers, leaving only one layer; and add a vacuum layer with a thickness of about to the direction perpendicular to the single-layer graphene, so that the single-layer graphene is completely independent. Then expand the cell to obtain a classical graphene model with a six-membered ring network structure.

[0055] Referring to the drawings Figure 4 As shown in Fig. 2, next, cutting is performed. When the cutting plane only passes through the nodes of the carbon six-membered ring, a zigzag edge structure graphene nanoribbon is obtained; and when the cutting plane only passes through the carbon-carbon single bond of the carbon six-membered ring, an armchair edge structure graphene nanoribbon is obtained.

[0056] The width of the cut graphene nanoribbons is determined based on the position of the cutting plane. In this embodiment, the modeling selected is an armchair-shaped edge structure graphene nanoribbon with 10 columns of carbon atoms and a serrated edge structure graphene nanoribbon with 6 columns of carbon atoms. The two have similar widths, respectively. and

[0057] See attached document Figure 4 As shown, since the carbon atoms on the edge are unsaturated, in this embodiment, hydrogen atoms are suspended from the edge to saturate their chemical bonds.

[0058] Step 2: Optimize the structure using VASP software. (See attached document.) Figure 5 As shown, after exporting the model from MS software, it was exported using VESTA software into a POSCAR file format that can be used for calculations with VASP software. This file contains the positional information of each atom in the graphene nanoribbon model. (See attached document.) Figure 6 As shown, the platform for VASP calculation is a supercomputer. In this embodiment, VASP calculation requires a parameter setting file INCAR, an atomic coordinate file POSCAR, an atomic pseudopotential file POTCAR, and a K-point selection file KPOINTS.

[0059] The INCAR file is a parameter setting file for the calculation, specifying the accuracy of the calculation. Many parameters can be set in the INCAR file, including the definition of the optimization method and the setting of the convergence criterion. In this embodiment of the invention, the main parameters set are the cutoff energy ENCUT, the maximum number of iterations for the energy self-consistent field NELM, the maximum permissible error EDIFF, the relaxation termination condition EDIFFG, and whether to output charge density-related files. Generally speaking, a larger cutoff energy indicates more plane-wave basis sets used to describe the wavefunction, resulting in higher calculation accuracy but also longer calculation time. The maximum number of iterations for the energy self-consistent field specifies the termination condition to avoid long calculation times. The maximum permissible error EDIFF is the condition for determining self-consistency during the self-consistent iteration calculation of the electronic structure part; a smaller value results in higher accuracy but longer calculation time. EDIFFG controls the relaxation of the ion part. When the total energy change of ion relaxation in the previous and current steps is less than EDIFFG, ion relaxation stops; it is often a very small negative number, controlling the forces experienced by ions and atoms during ion relaxation.

[0060] POTCAR defines the pseudo-potential file of each atom in the model, which is mainly selected from the VASP database and combined as needed. In the pseudo-potential approximation, the complex potential generated by the atomic nucleus and electrons (i.e. non-valence electrons) and the atomic nucleus is replaced by an "effective potential" (pseudo-potential), and the Coulomb potential term in the Schrödinger equation becomes an effective potential term that facilitates the next step of calculation. The constructed pseudo-potential replaces the potential generated by all electrons in the atom, simplifying the state of the atomic center, so that the valence electrons can be described by pseudo-wave functions containing fewer nodes. In short, the pseudo-potential provides the "electronic potential state" around each single atom, and the pseudo-potential approximation is a simplification method that makes the overall potential computable. VASP provides multiple pseudo-potential files for each atom, and in the selection of pseudo-potentials, the US-type pseudo-potential requires a smaller cutoff energy and has a fast calculation speed, while the PAW pseudo-potential generally has a larger cutoff energy and considers more electrons, resulting in slower calculations. However, for structures composed of elements with different atomic radii, PAW pseudo-potentials are more accurate than ultra-soft pseudo-potentials. The graphene nanoribbon of the present embodiment uses edge-hanging hydrogen atoms to treat edge-hanging bonds, involves two different elements, and therefore PAW pseudo-potentials are selected. The generalized gradient approximation GGA is suitable for calculating surface structures that are not dense (such as graphene), so the exchange-correlation energy function is calculated using GGA. The functional selected is the PBE functional in the generalized gradient approximation (GGA-PBE).

[0061] KPOINTS is a file that specifies K points. In the process of atomic relaxation and charge density calculation, the selection of K points mainly determines the grid density, thereby determining the calculation accuracy.

[0062] After setting the above parameters, submit to the supercomputer for running, refer to the attached Figure 6 The left part shows the INCAR file used by the software VASP during structure optimization. The system reads the relevant parameters in INCAR, including the number of iterations, iteration accuracy, etc., and then adjusts the atomic coordinates repeatedly through iteration according to the first principles until the system energy converges to a minimum value. The result obtained is the atomic coordinates corresponding to the ground state graphene nanoribbon. Refer to the attached Figure 6 The right part shows that the result is output in the form of a CONTCAR file, obtaining the optimized graphene nanoribbon structure.

[0063] Step 3, static self-consistent calculation, through iteration to obtain the converged charge density and electron wave function. The theory used in this step is the density functional theory, which obtains the ground state electron wave function and charge density distribution by solving the Schrödinger equation.

[0064] According to Bloch's theorem, for a periodic system, the electron wave function can be written as the product of a unit cell part and a Bloch part, where is the wave vector, is the position vector:

[0065]

[0066] where the electronic wave function of the unit cell can be expressed by a set of plane waves in reciprocal space, is the reciprocal lattice vector in reciprocal space:

[0067]

[0068] Thus, the electronic wave function can be written as a sum of plane waves:

[0069]

[0070] According to the density functional theory, the electronic wave function is determined by solving the Kohn-Sham equation:

[0071]

[0072] where ε i is the Kohn-Sham eigenvalue, V ion is the potential between the electron and the nucleus. V H and V XC are the Hartree potential and the exchange-correlation potential of the electron, respectively, and their expressions are as follows:

[0073]

[0074] According to the above principle, the flow of iterative calculation is shown in Figure 2 Similar to the process of step 2 structure optimization, the obtained CONTCAR file after optimization is named as POSCAR as the new structure information, and after giving the parameters such as the maximum number of iterations and the cutoff energy in the file INCAR, the static self-consistent calculation can be performed. VASP will first generate the trial charge density and the trial electronic wave function, write the expression of the exchange correlation potential based on it, and construct the Hamiltonian according to the charge density. Then through the methods of subspace diagonalization, iterative diagonalization, etc., the electronic wave function is iteratively optimized to be closer to the exact electronic wave function of the Hamiltonian. Then the new charge density is calculated according to the optimized electronic wave function, and then it is compared with the old trial charge density. If the result converges, the electronic wave function and the charge density are output; if the result does not reach the convergence accuracy, another round of calculation is performed until the result reaches the convergence accuracy or the number of iterations reaches the maximum value set.

[0075] In the specific calculation, the graphene nanoribbon model optimized in step 2 is input as a POSCAR file, INCAR is reset, and the input file is complete to start the iterative calculation. The POTCAR pseudo-potential file and the KPOINTS file used are consistent with step 2. Finally, the charge density and electron wave function of the ground state graphene nanoribbon are obtained, wherein the charge density data is stored in the CHG and CHGCAR files, and the electron wave function data is stored in the WAVECAR file, which is used for the next step calculation.

[0076] Step 4, calculate the electronic density of states, band structure and optical properties. The electronic wave function calculated in step 3 (stored in the WAVECAR file) can be used to calculate the electronic density of states and band structure. The band structure (i.e. dispersion curve E k ) in the graphene nanoribbon material can be expressed as:

[0077] E k = V F hk

[0078] In the formula, V F is the Fermi velocity of graphene, h is the Planck constant, and k is the electron wave vector.

[0079] The electron velocity in a general material is expressed as:

[0080]

[0081] However, the Fermi surface velocity effective mass m* of the 2PZ electron in graphene is infinitely close to 0, so the electron in graphene is a Dirac fermion.

[0082] In the specific calculation, the WAVECAR file calculated in step 3 is input, and INCAR is set to start the calculation, wherein POSCAR and POTCAR are consistent with step 3. It should be noted that KPOINTS changes in meaning, which is no longer the density of reciprocal lattice grid, but the path for calculating the band, which requires spanning the entire Brillouin zone. In the embodiment of the method, since the graphene nanoribbon is a quasi-one-dimensional material, the calculation path determined by KPOINTS needs to cover x, y and z directions.

[0083] The calculated electronic density of states and band structure data are output in the vasprun.xml file, and the data are extracted and plotted to obtain the band structure of the graphene nanoribbon as shown in FIG. 2B and FIG. 2C. Figure 7 and FIG. 2C. Figure 8The electronic state density and the band structure diagram are shown. As can be seen from the figure, the armchair edge structure graphene nanobelt has a certain band gap and belongs to a semiconductor structure; and the zigzag edge structure graphene nanobelt has no band gap and has metallicity. These are consistent with the results obtained by existing research, proving the rationality of the calculation method in the application.

[0084] The optical properties can be calculated using the obtained charge density. After the light propagates in the graphene, the optical properties such as absorption, reflection, etc. are generated. The optical properties of the graphene can be described by the collision between particles and particles, the light beam with momentum and energy, composed of photons, irradiated onto the graphene crystal, the photons of the incident light will collide with the molecules in the graphene crystal, so that the momentum and energy between the two will change, which determines the special optical properties of the graphene. The optical spectrum of the graphene crystal is calculated by the first principle, and the energy and momentum of the graphene molecules are described according to the frequency and amplitude corresponding to the peak of reflection and absorption. The spectral information of reflection and absorption can also be used to specifically characterize the energy spectrum of various molecules in the graphene crystal, including molecular vibration spectrum, graphene electronic energy level, etc. The strength of the incident light photon and the excitation and the degree of mutual coupling between them can be used to determine the optical properties of the graphene crystal and the strength of the reflection and absorption spectrum peak.

[0085] When the incident light propagates in the graphene crystal, it will attenuate, which can be expressed by the following formula:

[0086] I = I0e -αd

[0087] Wherein, d represents the propagation distance of the incident light in the graphene crystal, and a represents the absorption coefficient.

[0088] The dielectric function is a very important parameter for calculating the optical properties of the graphene crystal by the first principle, and the dielectric function can be used to calculate other optical properties:

[0089] ε r = n 2 -k 2

[0090] ε i = 2nk

[0091] The complex refractive index is:

[0092] N = n + ik

[0093] The absorption coefficient is:

[0094]

[0095] The absorption rate is:

[0096] A = a d

[0097] The reflectivity of the graphene crystal is:

[0098]

[0099] Wherein, n represents the refractive index, and k represents the extinction coefficient.

[0100] With the charge density information (stored in CHG and CHGCAR files) calculated in step 3 as a known quantity, the optical properties of the single-layer graphene model can be calculated after setting the corresponding parameters, and the calculation examples provided by the present application include the dielectric function (see FIG. 1), the absorption coefficient, the absorption rate, the reflectivity, the transmissivity and the energy loss. Figure 9 Specifically, the dielectric function is first obtained on the basis of the charge density, and then the real part and the imaginary part matrix of the dielectric function are obtained; further, the absorption rate, the reflectivity, the transmissivity, the energy loss spectrum and other optical properties of the graphene nanobelt can be calculated by using VASPKIT to post-process the real part and the imaginary part matrix of the dielectric function, and the calculation results are shown in FIG. 1. Figure 10-13

[0101] In summary, the present application provides a method for calculating the energy band structure and optical properties of a graphene nanobelt: an independent graphene nanobelt model is established by cutting and adding a vacuum layer; the structure of the graphene nanobelt is optimized by using the first principle; the electronic wave function and the charge density of the graphene nanobelt are self-consistently calculated by using the density functional theory; finally, the energy band structure and the state density are obtained by using the electronic wave function, and the optical properties such as the dielectric function are calculated by using the charge density. This method can theoretically deduce the optical properties of a graphene nanobelt with a specific structure, is highly innovative, and expands experimental measurements based on rigorous theoretical analysis and calculation, and is especially suitable for cases where it is difficult to make narrow graphene nanobelts, and can reasonably predict the performance thereof. On the basis of the present application, the optical properties of graphene nanobelts with different widths and edge structures are further studied, thereby providing a method for more profound application of graphene materials in the optical field.

[0102] In addition, the foregoing merely illustrates some embodiments, which can be changed, modified, added and / or varied without departing from the scope and essence of the disclosed embodiments, and the embodiments are illustrative rather than limiting. In addition, the described embodiments relate to currently considered most practical and most preferred embodiments, which should be understood as embodiments should not be limited to the disclosed embodiments, but rather, are intended to cover different modifications and equivalent arrangements within the essence and scope of the embodiments. In addition, the above-described various embodiments can be applied together with other embodiments, for example, aspects of one embodiment can be combined with aspects of another embodiment to achieve another embodiment. In addition, each independent feature or component of any given component can constitute another embodiment.​

[0103] The foregoing description of embodiments is provided for illustrative and explanatory purposes and is not intended to be exhaustive or limiting of this disclosure. Elements or features of a particular embodiment are generally not limited to that particular embodiment, but where applicable, elements or features are interchangeable and can be used in alternative embodiments, and can be modified in various ways, even if not specifically shown or described. Such modifications are not considered a departure from this disclosure, and all such modifications are included within the scope of this disclosure.

[0104] Therefore, it should be understood that the accompanying drawings and description provided herein by way of example are intended to aid in the understanding of the invention and should not be construed as limiting its scope.

Claims

1. A method for predicting the band structure and optical properties of graphene nanoribbons, characterized in that, Includes the following steps: S1. Establish a graphene model by adding a vacuum layer, cutting, and suspending hydrogen atoms at the edges to construct the atomic structure model of graphene nanoribbons. S2, based on the atomic structure model of graphene nanoribbons, first-principles optimization was used to find the structure that minimizes the energy of the system, resulting in the optimized graphene nanoribbons. S3, using density functional theory to calculate the charge density and electronic wave function of the optimized graphene nanoribbons; S4. Calculate the band structure and electronic state density of the graphene nanoribbon based on the electronic wave function; calculate the optical properties of the graphene nanoribbon based on the charge density. The optical properties include dielectric function, absorptivity, reflectivity, transmittance, and energy loss spectrum. Step S1 specifically involves: The atomic structure model of graphene nanoribbons was constructed using the software Materials Studio: graphite crystals were introduced, the symmetry between graphite layers was eliminated, and excess graphite layers were removed, leaving one layer to form a monolayer graphene; a vacuum layer with a thickness of 20 Å was added in a direction perpendicular to the monolayer graphene to form a completely independent monolayer graphene, and the unit cell was expanded to obtain a graphene model with a six-membered ring network structure. When cutting graphene, if the cutting plane only passes through the nodes of the six-membered carbon ring, a serrated edge structure graphene nanoribbon is obtained; if the cutting plane only passes through the carbon-carbon single bonds of the six-membered carbon ring, an armchair-shaped edge structure graphene nanoribbon is obtained. The width of the obtained graphene nanoribbon is determined according to the position of the cutting plane. After the graphene nanoribbons are cut, hydrogen atoms are suspended on the carbon atoms with unsaturated valence bonds at the edges to saturate their chemical bonds; Step S3 includes obtaining the convergent charge density and electron wave function through static self-consistent calculation; the self-consistent calculation adopts density functional theory and obtains the ground state electron wave function and charge density distribution by solving the Schrödinger equation; The electron wave function is determined by solving the Kohn-Sham equations: in, Represents the electron wave function. ε i Represents the Kohn-Sham eigenvalues. V ion This represents the interaction potential between the electron and the nucleus. V H and V XC Let Hartree potential and exchange-correlation potential of electrons be represented respectively, and their expressions are as follows: 。 2. The method for predicting the band structure and optical properties of graphene nanoribbons according to claim 1, characterized in that, Step S2 includes exporting the atomic coordinate file POSCAR from the graphene nanoribbon model established by Materials Studio using the software VESTA, which becomes the initial calculation file for the software VASP. The initial calculation file is then imported into the software VASP, and structural optimization is performed using the software VASP to obtain the optimized graphene nanoribbon structure, which is then output in the form of a CONTCAR file.

3. The method for predicting the band structure and optical properties of graphene nanoribbons according to claim 2, characterized in that, The initial calculation file also includes the parameter setting file INCAR, the atomic pseudopotential file POTCAR, and the K-point selection file KPOINTS; when performing structural optimization using the software VASP, the PAW pseudopotential is selected, the exchange correlation energy function is calculated using GGA, and the functional is GGA-PBE.

4. The method for predicting the band structure and optical properties of graphene nanoribbons according to claim 3, characterized in that, The CONTCAR file obtained in step S2 is renamed POSCAR as the new structural information. The calculation parameters are given in the INCAR file, and static self-consistent calculation is performed using the VASP software. Generate the trial charge density and trial electron wave function, write the expression for the exchange correlation potential based on them, and construct the Hamiltonian based on the charge density; By diagonalizing the subspace or iteratively diagonalizing, the electronic wavefunction is iteratively optimized to make it closer to Hamilton's exact electronic wavefunction. The new charge density is calculated based on the optimized electron wave function, and then compared with the trial charge density. If the result converges, the electron wave function and charge density are output; if the result does not reach the convergence accuracy, another round of calculation is performed until the result reaches the convergence accuracy or the number of iterations reaches the set maximum value.

5. The method for predicting the band structure and optical properties of graphene nanoribbons according to claim 3 or 4, characterized in that, When performing static self-consistent calculations using the software VASP, the PAW pseudopotential is selected, the exchange correlation energy function is calculated using GGA, and the functional is GGA-PBE. The calculated charge density data of the ground-state graphene nanoribbons are stored in CHG and CHGCAR files, and the electronic wavefunction data is stored in WAVECAR file.

6. The method for predicting the band structure and optical properties of graphene nanoribbons according to claim 5, characterized in that, In step S4, the WAVECAR file is input into the VASP software, the INCAR file is set, and calculation is performed. During this process, KPOINTS means the path of the calculated band structure, which is required to cross the entire Brillouin zone. The calculated electronic density of states and band structure data are output in the vasprun.xml file. Extracting the data and plotting it yields the electronic density of states and band structure diagram.

7. The method for predicting the band structure and optical properties of graphene nanoribbons according to claim 6, characterized in that, In step S4, the dielectric function is obtained based on the charge density, and then the real and imaginary parts of the dielectric function are obtained; the absorptivity, reflectivity, transmittance and energy loss spectrum of the graphene nanoribbon are calculated using the real and imaginary parts of the dielectric function.

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